Metrology systems and methods for overlay metrology

Abstract

This invention discloses a metrology system comprising an imaging system. The imaging system may include an objective lens. The metrology system may include one or more detectors. The metrology system may include an objective lens positioning stage structurally coupled to the objective lens and configured to adjust the focal plane of at least one of the one or more detectors by moving along one optical axis of the metrology system. The metrology system may include one or more proximity sensors configured to measure the lateral position of a stage element as the objective lens positioning stage moves along the optical axis. The metrology system may be configured to use the images and lateral positions of the stage element when a metrology formulation is implemented to determine a metrological measurement associated with a target on a sample.

Description

Technical Field

[0001] The present invention relates generally to metrology, and more particularly, to alignment of metrology systems. Prior Art

[0002] In wafer fabrication, metrology is the field of measurement and can include overlay metrology, critical dimension metrology, and the like.

[0003] In wafer fabrication, as the number of layers increases and / or the height of individual layers increases (e.g., 3D NAND, die-to-wafer (D2W), wafer-to-wafer (W2W), and the like), the height range between layers and / or features of interest increases. Conventional metrology systems may not have the focal plane adjustment distance required to image multiple layers and / or features at increasingly greater distances from one another while remaining within the alignment tolerances of the imaging system. Furthermore, a metrology system may need to approach a target feature but may not have the speed and / or height adjustment range required to move away when moving to the next significantly higher target feature.

[0004] Overlay control is essential for controlling the pattern-to-pattern alignment of multiple layers. Image-based overlay metrology typically involves determining the relative overlay error (e.g., misalignment error) between two or more layers of interest on a sample (e.g., a wafer) based on the relative imaged positions of features of an overlay target in different layers of interest.

[0005] Therefore, systems and methods for addressing the above-mentioned shortcomings are desirable. Summary of the Invention

[0006] According to one or more illustrative embodiments of the present invention, a metrology system for high-precision metrology is disclosed. In one illustrative embodiment, the system includes an objective lens. In another illustrative embodiment, the system includes one or more detectors. In another illustrative embodiment, the system includes an objective lens positioning stage structurally coupled to the objective lens and configured to adjust a focal plane of at least one of the one or more detectors by moving along an optical axis, the metrology system including the optical axis. In another illustrative embodiment, the system includes one or more proximity sensors configured to measure the lateral position of a stage component as the objective lens positioning stage moves along the optical axis. In another illustrative embodiment, the metrology system is configured to capture images of two or more focal planes by moving the objective lens positioning stage along the optical axis to two or more objective lens positions, each of the two or more focal planes being located at an axial position along and orthogonal to the optical axis of the metrology system. In another illustrative embodiment, at least two of the two or more focal planes are separated by an axial focal length that is greater than a depth of field provided by the objective lens. In another illustrative embodiment, the metrology system is configured to use the images and lateral position of the objective positioning stage when the objective lens positioning stage is at the two or more objective lens positions when implementing a metrology recipe to determine a metrology measurement associated with an object on a sample, the object comprising features in the two or more focal planes according to the metrology recipe.

[0007] According to one or more illustrative embodiments of the present invention, a metrology system for high metrology using air bearings is disclosed. In one illustrative embodiment, the system includes a coarse positioning stage for an objective lens positioning stage, the coarse positioning stage being radially supported about an optical axis by one or more air bearings. The one or more air bearings are configured to allow longitudinal movement of the coarse positioning stage along the optical axis and to constrain lateral translation and tilt of the coarse positioning stage relative to the optical axis when adjusting a focal plane of one or more detectors.

[0008] According to one or more illustrative embodiments of the present invention, a method for high overlay metrology is disclosed. In one illustrative embodiment, the method includes receiving lateral positions of a stage element of a metrology system from one or more proximity sensors, the lateral positions measured relative to an optical axis. In another illustrative embodiment, the metrology system is configured to adjust a focal position of at least one of one or more detectors of the metrology system, wherein the metrology system is configured to capture images of two or more focal planes by moving an objective lens positioning stage along the optical axis to two or more objective lens positions, each focal plane of the two or more focal planes being at an axial position along and orthogonal to the optical axis of the metrology system, wherein at least two of the two or more focal planes are separated by an axial focal length that is greater than a depth of field provided by an objective lens. In another illustrative embodiment, the method includes receiving the images of the two or more focal planes by moving the objective lens positioning stage along the optical axis to the two or more objective lens positions. In another illustrative embodiment, the method includes using the images and lateral position of the stage element to determine a metrological measurement associated with a target on a sample when the objective positioning stage is at the two or more objective positions, the target including features on the two or more focal planes.

[0009] It should be understood that both the foregoing general description and the following detailed description are for illustration and explanation only and are not necessarily limiting of the present invention. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present invention and, together with the general description, serve to explain the principles of the present invention. Simple diagram description

[0010] Those skilled in the art may better understand the advantages of the present invention by referring to the accompanying drawings. FIG. 1A is a diagram illustrating a metering system according to one or more embodiments of the present invention. FIG. 1B is a diagram illustrating a metering system according to one or more embodiments of the present invention. FIG. 1C illustrates a diagram of a metrology system having two or more detectors according to one or more embodiments of the present invention. 2A is a diagram of an imaging system in a first position according to one or more embodiments of the present invention. 2B illustrates a diagram of the imaging system in a second, misaligned position, in accordance with one or more embodiments of the present invention. 2C illustrates a diagram of the imaging system in a third position at least partially corrected by a fine adjustment stage in accordance with one or more embodiments of the present invention. 3A is a diagram of an imaging system in a first position according to one or more embodiments of the present invention. 3B illustrates a diagram of the imaging system in a second, misaligned position, in accordance with one or more embodiments of the present invention. 3C illustrates a diagram of the imaging system in a third position at least partially corrected by a coarse adjustment stage in accordance with one or more embodiments of the present invention. FIG. 4 illustrates a flow chart of a method for overlay metrology according to one or more embodiments of the present invention. Implementation Method

[0011] The present invention has been particularly shown and described with respect to specific embodiments and features thereof. The embodiments described herein are to be considered illustrative rather than restrictive. Those skilled in the art will readily appreciate that various changes and modifications in form and detail may be made without departing from the spirit and scope of the present invention. Reference will now be made in detail to the disclosed subject matter illustrated in the accompanying drawings.

[0012] Referring generally to Figures 1-4 , systems and methods for high metrology according to one or more embodiments of the present invention are disclosed. Embodiments of the present invention are directed to providing a metrology system capable of high metrology. High metrology can include any type of metrology known in the art (e.g., critical dimension (CD) metrology, conventional overlay metrology, scatterometry overlay metrology (SCOL), diffraction-based overlay (DBO), and / or the like), such as (but not limited to) single wafer, D2W, W2W, and / or the like with features spaced apart and / or with relatively distant (e.g., greater than 15 microns) focal lengths. It should be noted that some embodiments of the present invention enable high metrology by utilizing one or a combination of the following: increased focal plane adjustment distance capability, increased focal plane axial position change speed, alignment sensors (e.g., proximity sensors), stage element adjustment stages, and / or more accurate alignment structures (e.g., thin flexure arms and / or air bearings). In at least some embodiments, benefits of one or a combination of the above may include: more accurate overlay error (e.g., offset measurement between features in different layers of a sample), more accurate critical dimensions (e.g., location and / or size of a feature) in a CD metrology system, faster movement of the focal plane, more accurate alignment of optical elements of a metrology system, a greater range of focal plane adjustment distances, and the like.

[0013] Some embodiments of the present invention are directed to a metrology system having a device for measuring one or more lateral positions of a stage component of the metrology system to at least determine / generate a misalignment of the stage component. For example, one or more proximity sensors may allow determination of one or more lateral measurements that can be used to measure a misalignment of a stage component (e.g., lateral offset and / or tilt).

[0014] For example, generally, some embodiments of the present invention are directed to a metrology system having an objective lens, one or more detectors, an objective lens positioning stage, and one or more proximity sensors. For example, the objective lens positioning stage may be structurally coupled to (or include) the objective lens and configured to adjust a focal plane of at least one of the one or more detectors by moving along an optical axis of the metrology system. In another example, the metrology system may be configured to capture images of two or more focal planes by moving the objective lens positioning stage along the optical axis (e.g., when adjusting a focal plane) to two or more objective lens positions, each of the two or more focal planes being located at an axial position along and orthogonal to the optical axis of the metrology system. For example, at least two of the two or more focal planes may be separated by an axial focal length that is greater than the depth of field provided by the objective lens (e.g., not all features located at all focal planes are simultaneously in focus). In another example, or continuing with the above example, a metrology system (e.g., an overlay metrology system, a critical dimension (CD) metrology system, or the like) can be configured to use images and lateral positions of stage elements to determine a metrology measurement (e.g., overlay error, critical dimension, and the like) associated with a target (e.g., an overlay target, a critical dimension target, and the like) on a sample when the objective lens positioning stage is at two or more objective lens positions (e.g., corresponding to two or more focal planes), and the target can include features (e.g., overlay target features, or any other features to be measured) at two or more focal planes according to a metrology recipe.

[0015] Furthermore, with respect to the above examples, embodiments may be directed to a metrology system having an imaging system(s) and one or more detectors configured to capture images through an objective lens at two or more focal positions along an optical axis of the imaging system, wherein one or more proximity sensors measure one or more lateral positions of a stage component of the metrology system (e.g., a coarse positioning stage, a fine positioning stage, or the like). For example, in one non-limiting example, the one or more proximity sensors may measure one or more lateral positions of a coarse positioning stage, and the one or more lateral positions may be used to at least partially correct for an inaccuracy in a metrology measurement of a sample caused by at least one of a measured coarse positioning stage lateral offset or a measured coarse positioning tilt. In another example, the one or more proximity sensors may measure one or more lateral positions of a fine positioning stage, and the one or more lateral positions may be used to at least partially prevent an inaccuracy in a metrology measurement by mechanically compensating for a misalignment in the measured one or more lateral positions before capturing the measurement image. At least some benefits of at least some embodiments include faster focus adjustment, more accurate alignment during focus adjustment, and / or a wider range of focus adjustment (e.g., which may be made possible by more accurate stage component alignment). For example, at least some embodiments allow (e.g., mathematically) at least partially correcting (or preventing / compensating for) optical axis misalignment of one or more components (e.g., stage components) of an imaging system by (but not limited to) mechanically adjusting a calculated / determined metrology measurement based on a measured offset of a stage component, or mechanically adjusting (e.g., directing imaging system adjustment) a mechanical component to at least partially correct (e.g., compensate for) a measured offset of a stage component (e.g., a coarse positioning stage, a fine positioning stage, and the like). It should be noted that the term "stage component" is not limited to the term "stage" and may also include any stage component of a metrology system, such as an objective (e.g., an objective subsystem), a frame, or the like.

[0016] Additional embodiments are directed to a metrology system having an imaging system with thin flexure arms supporting a stage element of the imaging system. For example, some embodiments of the present invention are directed to a metrology system including an imaging system having two or more thin flexure arms supporting a fine positioning stage. The thin flexure arms can be configured to allow longitudinal movement of the fine positioning stage along an optical axis and to constrain lateral translation and tilt of the fine positioning stage relative to the optical axis when adjusting the focus position of a detector. At least some benefits include speed, accuracy (i.e., reduced misalignment relative to the optical axis), and a greater range of height adjustment (e.g., focal plane adjustment distance). Furthermore, misalignment of the fine positioning stage is repeatable. In an optional configuration, one or more proximity sensors are used to measure one or more lateral positions of a stage element at different focus positions associated with a movement of the fine positioning stage. Furthermore, a calibration of a repeatable misalignment error (e.g., lateral offset and / or tilt) of the fine positioning stage can be determined. Furthermore, the calibration can be used to at least partially correct a metrology measurement. For example, calibration may be used to mathematically correct metrological measurements and / or mechanically correct metrological measurements (e.g., using a fine adjustment stage).

[0017] Further embodiments are directed to metrology systems having an imaging system with one or more bearings supporting a stage element of the imaging system. For example, some embodiments of the present invention are directed to a metrology system including an imaging system having one or more air bearings supporting a coarse positioning stage. The air bearings can be configured to allow longitudinal movement of the coarse positioning stage along an optical axis while constraining lateral offset and tilt of the coarse positioning stage relative to the optical axis when adjusting the axial position of a detector's focal plane (e.g., moving the coarse positioning stage). In some embodiments, at least some benefits include speed, accuracy (i.e., reduced misalignment relative to an optical axis), and a greater range of height adjustment (e.g., focus position height adjustment).

[0018] Additional embodiments are directed to metrology systems having an imaging system with two or more detectors (e.g., cameras) and at least one of a thin flexure arm, an air bearing, and / or two or more proximity sensors. For example, some embodiments of the present invention are directed to a metrology system comprising an imaging system with two or more detectors, wherein the imaging system comprises one or more proximity sensors and at least one of 1) two or more thin flexure arms or 2) one or more air bearings supporting a stage element (e.g., a fine positioning stage and / or a coarse positioning stage).

[0019] It should be noted that a determined (e.g., calculated, generated, and the like) metrology measurement itself can be inaccurate due to a variety of reasons. For example, a metrology measurement can be inaccurate due to, but not limited to, a lack of resolution and / or focus of the imaging tool, or misalignment (e.g., drift over time and / or drift caused by operation of the imaging system (e.g., changes in the axial position of a stage element)) of one or more components of the imaging system (e.g., stage element). For example, an error (e.g., inaccuracy) in a metrology measurement can be a combination of, but not limited to, an offset caused by adjusting the axial position of a stage element (e.g., fine positioning stage, coarse positioning stage, and the like), an offset due to flexibility (e.g., non-rigidity) in an imaging system element (e.g., a frame or rigid plate), an offset due to an unconstrained tolerance gap between two or more imaging system elements (e.g., the gap between a coarse positioning stage and the bearing supporting the coarse positioning stage), tool-induced offset (TIS), an offset caused by environmental and / or metrology system vibration (e.g., jitter), and the like. These errors in metrology measurements can affect the measurement efficiency / accuracy of the metrology process and, therefore, the manufacturing and / or inspection process of a sample. These errors can also limit the maximum focal plane adjustment distance (measured between features) of a metrology system, as increasing the maximum focal plane adjustment distance (e.g., without the benefit of the present invention) can cause the metrology system to have an unacceptable alignment error, resulting in an unacceptable inaccuracy in the metrology measurement (e.g., outside of tolerance specification requirements).

[0020] It should be noted that a focal plane refers to the plane or volume focused by an imaging system (e.g., imaging system 104). For example, an imaging system may be capable of a range of focal planes spanning a maximum focal plane adjustment distance of the imaging system via a positioning stage (e.g., an objective lens positioning stage). At least some embodiments of the present invention allow for an imaging system 104 with an increased maximum focal plane adjustment distance that is adjustable within desired alignment tolerances. For example, in some embodiments, the present invention allows for a metrology system 100 with a maximum focal plane adjustment distance of at least 1000 microns (e.g., by achieving overlay metrology for measurement of offset between layers superimposed at a distance of at least 1000 microns) while operating within tolerances of 3 nanometers for lateral offset and 3 microradians for tilt.

[0021] Furthermore, the maximum focal plane adjustment distance required between different focal planes of different features (e.g., as measured perpendicular to a wafer surface (e.g., the wafer surface facing the imaging system) and / or parallel to an ideal / design optical axis) can increase due to factors including, but not limited to, an increase in the total number of layers per sample and higher individual layer heights (e.g., 3D NAND, Thin Film Heads (TFH)). In this regard, a stage element may need to travel a distance corresponding to a maximum focal plane adjustment distance (e.g., as measured between the focal plane of the metrology system and / or features of the sample) and / or an axial adjustment distance (e.g., the distance the stage source moves along the optical axis) that is greater than the distance a conventional system can travel. The inability to travel this corresponding distance can include, but is not limited to, inadvertently contacting a tall target feature while traversing the sample, and the inability to effectively and / or fully accurately image tall (high) and short (low) target features (e.g., due to a lack of focus adjustment range).

[0022] Therefore, embodiments of the present invention are directed to a system and method that addresses one or more of the shortcomings of previous approaches.

[0023] FIG1A illustrates a diagram of a metrology system according to one or more embodiments of the present invention. For example, the metrology system 100 can determine metrology measurements between two or more layers of a sample 102 based on an image of one or more features of the sample 102 according to a metrology recipe.

[0024] In one embodiment, the metrology system 100 includes an imaging system 104 configured to capture one or more images of a sample 102 and a controller 106 that determines metrology measurements of two or more layers of the sample 102 based on the images from the imaging system 104 according to a metrology recipe. Furthermore, the metrology system 100 may include a sample stage 108 for positioning the sample 102 within a field of view of the imaging system 104 (e.g., an area beneath an objective lens) to determine metrology measurements. The sample stage 108 may include any system suitable for positioning the sample 102 within the metrology system 100. For example, the sample stage 108 may include any combination of a linear translation stage, a rotation stage, a tip / tilt stage, or the like.

[0025] In at least one embodiment, the metrology system 100 may include one or more imaging systems 104. In another embodiment, the metrology system 100 may include, but is not limited to, a controller 106 having one or more processors 110 and a memory 112, and a sample stage 108. The imaging system 104 may include any imaging system 104. In one embodiment, the controller 106 is communicatively coupled to an imaging system 104 (such as the imaging system 104 shown in FIG. 1B and described in detail below). In this regard, the one or more processors 110 of the controller 106 may be configured to generate one or more control signals configured to adjust one or more characteristics of the imaging system 104 according to a metrology recipe.

[0026] FIG. 1B is a diagram illustrating a metering system according to one or more embodiments of the present invention.

[0027] In one embodiment, the metrology system 100 includes an illumination source 114 for generating an illumination beam 116, an illumination path 118 (which may be one or more illumination optics) for directing the illumination beam 116 (e.g., at least a portion of the light of the illumination beam) toward a sample 102 mounted on a sample carrier 108, and a collection path 142 for directing radiation emitted from the sample 102 toward a detector assembly 122. For example, the detector assembly 122 may include one or more detectors suitable for capturing an image of the sample 102. The optical axis of the imaging system may be split into multiple optical axes for each detector or may be separate optical axes.

[0028] Illumination beam 116 may include light of one or more selected wavelengths, including, but not limited to, vacuum ultraviolet radiation (VUV), deep ultraviolet radiation (DUV), ultraviolet (UV), visible light, SWIR, or infrared (IR). Illumination source 114 may further generate an illumination beam 116 comprising any range of selected wavelengths. In another embodiment, illumination source 114 may include a spectrally tunable illumination source to generate an illumination beam 116 having a tunable spectrum. Illumination source 114 may further generate an illumination beam 116 having any temporal profile. For example, illumination source 114 may generate a continuous illumination beam 116, a pulsed illumination beam 116, or a modulated illumination beam 116. Furthermore, illumination beam 116 may be transmitted from illumination source 114 via free-space propagation or guided light (e.g., an optical fiber, a light pipe, or the like).

[0029] The illumination source 114 may include any type of illumination source suitable for providing an illumination beam 116. In one embodiment, the illumination source 114 is a laser source. For example, the illumination source 114 may include, but is not limited to, one or more narrowband laser sources, a broadband laser source, a supercontinuum laser source, a white light laser source, etc. In this regard, the illumination source 114 may provide an illumination beam 116 having high coherence (e.g., high spatial coherence and / or high temporal coherence). In another embodiment, the illumination source 114 includes a laser sustained plasma (LSP) source. For example, the illumination source 114 may include, but is not limited to, an LSP lamp, an LSP bulb, or an LSP chamber suitable for housing one or more elements that emit broadband illumination when excited into a plasma state by a laser source. In another embodiment, the illumination source 114 includes a lamp source. For example, the illumination source 114 may include, but is not limited to, an arc lamp, a discharge lamp, an electrodeless lamp, etc. In this regard, the illumination source 114 may provide an illumination beam 116 having low coherence (eg, low spatial coherence and / or temporal coherence).

[0030] In another embodiment, the illumination source 114 directs an illumination beam 116 toward a sample 102 via an illumination path 118. For example, the illumination path 118 may include an objective lens 124 to focus the illumination beam 116 onto the sample 102. The illumination path 118 may include one or more illumination optics having one or more illumination path lenses 126 and / or illumination adjustment components 128 suitable for modifying and / or adjusting the illumination beam 116. For example, the one or more illumination adjustment components 128 may include, but are not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. As another example, the illumination path 118 may include an aperture stop to control the angle of illumination on the sample 102 and / or a field stop to control the spatial extent of illumination on the sample 102.

[0031] In another embodiment, collection path 142 (which may be one or more collection optics) may include any number of stage elements to collect radiation emitted from the sample (e.g., in response to illumination beam 116) and direct the collected radiation (e.g., collection beam 120) to detector assembly 122. In one embodiment, collection path 142 includes a beam splitter 134 oriented so that objective lens 124 can simultaneously direct illumination beam 116 toward sample 102 and collect radiation from sample 102. Collection path 142 may include one or more collection path lenses 136 and / or conditioning collection components 138 suitable for modifying and / or conditioning radiation from sample 102, such as, but not limited to, one or more filters, one or more polarizers, or one or more beam blocks. Additionally, collection path 142 may include an aperture stop to control the angular range of radiation collected from sample 102 and / or a field stop to control the spatial range of the image of sample 102. In another embodiment, collection path 142 includes an aperture stop. For example, the aperture stop may include a collection aperture stop located in a plane conjugate to the focal plane behind objective lens 124 and / or a tube lens (not shown) to provide image-space telecentricity when imaging sample 102. As another example, the aperture stop may include a collection field stop located in a plane conjugate to sample 102 to control the spatial extent of the image on detector assembly 122. Furthermore, collection path 142 may include any number of illumination path lenses 126 that facilitate placement of aperture stops and collection field stops at convenient locations.

[0032] Detector assembly 122 may include any number of detectors suitable for capturing radiation emitted from sample 102. For example, detector assembly 122 may include one or more imaging detectors suitable for generating an image at a selected focal position. For example, imaging detectors may include, but are not limited to, a charge-coupled device (CCD), a complementary metal-oxide semiconductor (CMOS) device, a time-delay imaging (TDI) detector, one or more photomultiplier tubes (PMTs), one or more avalanche photodiodes (APDs), or the like. In another embodiment, detector assembly 122 may include a spectral detector suitable for identifying the wavelength of radiation emitted from sample 102. In another embodiment, detector assembly 122 may include a short-wave infrared (SWIR) detector. For example, detector assembly 122 (e.g., detector) is a SWIR detector employing quantum dot technology. In another example, detector assembly 122 (e.g., detector) is a SWIR focal plane array (FPA).

[0033] The one or more illumination optics can be configured to direct illumination (e.g., illumination beam 116) from an illumination source 114 to a sample 102 through the objective lens 124 when implementing a metrology recipe, wherein, according to the metrology recipe, the sample 102 can include one or more first target features and one or more second target features, wherein the one or more first target features and the one or more second target features can be separated by a focal plane adjustment distance measured between the target features and which can be greater than a depth of field of the illumination provided by the objective lens 124.

[0034] Referring now to Figures 2A-3C , a metrology system is generally described that at least partially corrects for misalignment of stage components, prevents misalignment of stage components, and / or allows for high metrology. It should be noted that the components shown in Figure 2A are for illustrative purposes only, as compared to Figure 3A , and that, for example, an embodiment may include some or all components from both Figures 2A and 3A . For example, at least one embodiment of the metrology system includes both a fine adjustment stage 226 and a coarse adjustment stage 228 , while another embodiment includes neither fine adjustment stage 226 nor coarse adjustment stage 228 but includes proximity sensor 222 .

[0035] 2A-2B illustrate an imaging system 104 in a first position ( FIG. 2A ) and a second, lower (misaligned) position ( FIG. 2B ). FIG. 2C is similar to the imaging system 104 in the lower position of FIG. 2B , except that the misalignment (lateral offset and tilt) of the objective lens 218 is mechanically corrected by a fine adjustment stage 226 . It should be noted that the misalignment shown in FIG. 2A-3C is exaggerated for illustrative purposes, and that the imaging system 104 is still able to properly image the overlay target 202 (e.g., in focus and field of view) in the second position shown in FIG. 2B and FIG. 3B .

[0036] It should be noted that the position of imaging system 104 in Figures 3A-3C is similar to that in Figures 2A-2C, except that the misalignment of objective lens 218 in Figures 3A-3C is mechanically corrected by a coarse adjustment stage 228 (shown near frame 204 and coarse adjustment stage 208) rather than a fine adjustment stage 226 (shown near objective lens 218 in Figures 2A-2C).

[0037] FIG. 2A illustrates a diagram of an imaging system 104 in a first position (eg, first focus position / configuration) in accordance with one or more embodiments of the present invention.

[0038] The metrology system 100 may include an imaging system 104 and a sample stage 108. The metrology system 100 may include an objective lens 218, one or more detectors, an objective lens positioning stage, and / or one or more proximity sensors 222.

[0039] For example, the imaging system 104 may include: an objective lens 218; one or more detectors configured to capture images through the objective lens 218 at two or more focal positions along an optical axis 210 of the imaging system 104; a detector of the one or more detectors; and one or more illumination optics configured to direct illumination from an illumination source through the objective lens 218 toward a sample 102 when implementing a metrology recipe, wherein the sample 102 may include one or more first target features 202a and one or more second target features 202b according to the metrology recipe. Target features 202b, wherein one or more first target features 202a and one or more second target features 202b can be separated by a focal plane adjustment distance that can be greater than a depth of field of an objective lens 218; a coarse positioning stage 208, which is structurally coupled to a fine positioning stage 212; the fine positioning stage 212, which is structurally coupled to the objective lens 218; and one or more proximity sensors 222, which are configured to measure a lateral position of a stage element, wherein the stage element is at least one of the fine positioning stage 212 or the coarse positioning stage 208.

[0040] In at least one embodiment, imaging system 104 can be configured to allow a maximum focal plane adjustment distance. The maximum focal plane adjustment distance can be at least one of a maximum coarse adjustment and a maximum fine adjustment, or a combination thereof. For example, the maximum height difference between target features that a metrology system can capture in focus can be limited by a combination of a coarse adjustment (e.g., a coarse focal plane adjustment distance) provided by coarse positioning stage 208 and a fine adjustment (e.g., a fine focal plane adjustment distance) provided by fine positioning stage 212.

[0041] In one embodiment, a sample 104 comprising one or more layers and one or more target features 202 (e.g., one or more first target features 202a and one or more second target features 202b) can be imaged by an imaging system 104. For example, a target may include one or more first layer features 202a on a first layer of the sample 102 and multiple second layer features 202b on a second layer of the sample 102. In this regard, metrology measurements (i.e., offset / misalignment) between the first and second layers can be determined based on the relative positions of the first layer features 202a and the second layer features 202b. For example, according to a metrology recipe, a target may include features 202 on two or more focal planes of the metrology system 100. For example, a first focal plane may be aligned with the first layer features 202a.

[0042] In some embodiments, the imaging system 104 may include a frame 204. For example, the frame 204 may structurally support one or more coarse positioning stage support elements 206 (e.g., bearings 206).

[0043] For example, one or more coarse positioning stage support elements 206 may be one or more bearings 206, which may be one or more air bearings 206, roller bearings 206, or the like. In this regard, air bearings 206 may provide support (e.g., structural) to coarse positioning stage 208 with a tight tolerance. In one example, one or more bearings 206 (e.g., air bearings) may be operably coupled to coarse positioning stage 208. For example, one or more bearings 206 (e.g., air bearings) may constrain coarse positioning stage 208 along optical axis 210 (e.g., allowing longitudinal movement along optical axis 210 and constraining lateral movement and tilt of coarse positioning stage 208 relative to optical axis 210). In another example, when fine positioning stage 212 is structurally supported by coarse positioning stage 208, the alignment of fine positioning stage 212 may be dependent on the alignment of coarse positioning stage 208. For example, one or more bearings 206 may structurally support fine positioning stage 212 by supporting a coarse positioning stage 208 that structurally supports fine positioning stage 212, and the alignment tolerance of fine positioning stage 212 may vary based on the alignment tolerance of coarse positioning stage 208. In this regard, one or more bearings 206 may structurally support coarse positioning stage 208 for up and down movement in the vertical Z direction with an error of equal to or less than + / - 2.5 nanometers in the X and Y directions.

[0044] It should be understood that a target can include one or more target features 202 (e.g., according to a metrology recipe). It should be understood that an overlay target can generally be formed from any number of cells, and any particular cell can include a grating-on-grating feature having a periodicity along any direction. For example, sample 102 can include an overlay target formed from one or more cells, each cell including a grating-on-grating structure formed from grating structures on two layers of sample 102 according to a metrology recipe (as shown in FIG. 2A ). For example, a target can include an upper target feature 202a and a lower target feature 202b. However, it should be understood that a target for a sample 102 is not limited by the description and figures herein. For example, a target can include target features 202 on any number of layers of sample 102 (e.g., 3 layers, 4 layers, 150 layers, or the like). As another example, target features 202 can be suitable for any selected pattern orientation for image-based metrology measurements (e.g., overlay metrology measurements). For another example, the overlay target may include, but is not limited to, a box-in-box (BiB) pattern, a circle-in-circle pattern, a grating-on-grating pattern, a grating-next-grating pattern, a non-periodic pattern, a one-dimensional target, an advanced imaging metrology (AIM) overlay target, a TAIM overlay target, an AIMid overlay target, and any other overlay target.

[0045] Referring generally to the metrology system 100 , in one embodiment, the imaging system 104 is configured to image a wafer-to-wafer (W2W) bonded sample, and the sample 102 is a W2W bonded sample 102 according to a metrology recipe.

[0046] In other embodiments, the imaging system 104 is configured to image a wafer-to-wafer (D2W) bonded sample, and the sample 102 is a D2W bonded sample 102 according to the metrology recipe.

[0047] As another example, an overlay target 202 (e.g., a BiB pattern, an AIM target, and the like) may include a D2W overlay target, in which the XY position of a die feature 202 in a higher layer overlaps (e.g., is equal (concentric)) with the XY position of a wafer feature 202 in a lower layer. In this example, the desired focal plane adjustment distance between the higher target feature 202a and the lower target feature 202b may be on the order of several hundred microns (e.g., at least 200 microns).

[0048] As another example, the overlay target 202 (e.g., a BiB pattern, an AIM target, and the like) may include a D2W overlay target, in which the XY position of a die feature 202 in a higher layer is not equal to (non-overlapping, side-by-side, and the like) the XY position of a wafer feature 202 in a lower layer. In this example, the desired focal plane adjustment distance between the higher target feature 202a and the lower target feature 202b may be on the order of several hundred micrometers (e.g., at least 200 micrometers).

[0049] As another example, the overlay target 202 (e.g., having overlapping features of different layers) may comprise a W2W target. In this example for hybrid bonding of wafers, the required focal plane adjustment distance between the upper target feature 202a and the lower target feature 202b may typically be low (e.g., a few microns). However, it is contemplated that in some embodiments, when a W2W sample is configured to be manufactured using additional lithography steps or using additional through-silicon via (TSV) steps, the present invention can achieve high metrology for the W2W sample, such that the required focal plane adjustment distance between features 202 is greater than that in a typical hybrid bonded W2W sample. For example, a method step or system 100 may be configured to generate a metrology measurement on a W2W sample 102 according to a metrology recipe using at least one of an additional lithography step or an additional TSV step, such that the sample requires high metrology (e.g., a vertical adjustment of at least 20 microns).

[0050] Coarse positioning stage 208 may be driven by a coarse positioning stage driver 214. Coarse positioning stage driver 214 may be any driver that provides a maximum coarse adjustment (e.g., the distance measured between focal planes) for coarse positioning stage 208 (or associated with coarse positioning stage 208). For example, coarse positioning stage driver 214 may be a linear motor. In another example, coarse positioning stage driver 214 may be a combination of a rotary motor that rotates a drive screw that directly or indirectly drives coarse positioning stage 208 through a range of coarse positioning stage axial adjustment distances (measured as the distance the coarse positioning stage moves along the optical axis). Coarse positioning stage driver 214 may be configured to provide a wide range of coarse positioning stage axial adjustment distances to coarse positioning stage 208, corresponding to a large maximum coarse adjustment (e.g., the distance between focal planes) (e.g., greater than a maximum fine adjustment). For example, coarse positioning stage drive 214 can provide (e.g., provide at least) a maximum coarse adjustment of 50 microns, 500 microns, 2000 microns (2 mm), or the like relative to a plane perpendicular to sample 102 and / or a direction parallel to optical axis 210. It should be noted that the combination of air bearing 206 and the large maximum coarse adjustment of coarse positioning stage drive 214 can allow for a relatively accurate (e.g., reduced misalignment of a field of view) metrology system 100 capable of high metrology. In some embodiments, the addition of one or more proximity sensors allows for at least one of the even more accurate and / or even higher metrology described in greater detail throughout this disclosure.

[0051] In another embodiment, a stage element (e.g., fine positioning stage 212 and / or objective lens 218, or other stage elements) may be supported by two or more thin flexure arms 216. For example, thin flexure arms 216 may be configured to allow fine movement of fine positioning stage 212 along optical axis 210 while constraining lateral translation and tilt of the fine positioning stage relative to optical axis 210. For example, such fine movement may be movement of the objective lens positioning stage along the optical axis to one of two or more objective lens positions, and may provide adjustment of one of two or more focal planes of one or more detectors of imaging system 104 (e.g., changing the focal plane height to focus an image of a feature 202 of sample 102).

[0052] It should be noted that in some embodiments, each of the two or more focal planes can be defined as an axial position along and orthogonal to the optical axis of the metrology system. For example, the focal plane can be further defined as the plane to be focused by one or more detectors positioned to capture an image at an image plane conjugate to the focal plane. For example, an objective lens positioning stage can be used to adjust the axial position of an objective lens to shift the focal plane, while in some embodiments, the conjugate image plane of one or more detectors may not be shifted. In this regard, the coarse positioning stage driver 214 and / or the fine positioning stage driver 220 of the object positioning stage can be configured to move a stage element (e.g., fine positioning stage 212, coarse positioning stage 208, or the like) longitudinally along the optical axis 210 to adjust the axial position of a focal plane of one or more detectors.

[0053] Continuing with the above example, or alternatively, in another example, thin flexure arms 216 can be flexible and positioned in a pattern that constrains (e.g., to within a few (e.g., three or five) nanometers or microradians) misalignment of a stage element (e.g., fine positioning stage 212) relative to optical axis 210 (or a field of view). For example, thin flexure arms 216 can be arranged in a parallelogram configuration as shown in FIG. 2A , with at least two thin flexure arms 216 on each side of the optical axis supporting the stage element. In this regard, the two or more thin flexure arms 216 can include a first subset of two or more thin flexure arms on a first side of the fine positioning stage, and a second subset of two or more thin flexure arms on a second side of the fine positioning stage, where the second side is opposite the first side relative to optical axis 210.

[0054] Continuing with the above example, or alternatively, in another example, thin flexure arm 216 may allow a maximum fine adjustment (measured between focal planes) of a stage element (or associated therewith) of 20 microns or greater. For example, thin flexure arm 216 may allow a maximum fine adjustment of at least (or up to) 50 microns. In another example, thin flexure arm 216 may allow a maximum fine adjustment of 100 microns or greater. In at least some embodiments, benefits of thin flexure arm 216 include one or more of a relatively large maximum fine adjustment, tight alignment tolerance (i.e., lateral offset and tilt), relatively fast adjustment using an actuator (e.g., fine positioning stage actuator 220, such as a piezoelectric device (PZT) actuator), and calibrable, repeatable misalignment errors. For example, an alignment error of coarse positioning stage 208 may be less repeatable (e.g., random) than an alignment error of a fine positioning stage (e.g., due to the repeatability / predictability of the thin flexure arm). For example, the fine positioning stage can follow a predictable misalignment path / profile during movement, which can be measured by one or more proximity sensors and stored in memory and used later (e.g., without measuring the misalignment) to predict fine positioning stage misalignment and correct (or mechanically prevent) an inaccuracy in metrology measurements. For example, a calibrated fine positioning stage can be used to predict a misalignment of 5 nanometers in the X direction when the fine positioning stage is at an axial position of 10 microns. This misalignment can be corrected mathematically or mechanically, for example, as described in more detail throughout this disclosure. In another example, the fine positioning stage driver 220 can be a piezoelectric device (PZT) configured to produce motion of the fine positioning stage when a voltage is applied to the PZT, where the PZT can be operatively and structurally coupled to the fine positioning stage.

[0055] It should be noted that "correcting overlay error," "correcting metrology," and similar terms (e.g., "at least partially" correcting a metrology measurement) may mean "correcting an error / inaccuracy in a metrology measurement" (e.g., because a metrology measurement may be an estimate of a real-world measurement of the misalignment of two or more target features 202 (or the position or size of one or more sub-target features 202), whose accuracy is limited by the alignment and accuracy of the imaging system 104). Therefore, "correcting metrology measurements" and similar terms do not necessarily mean physically correcting a shift / defect in a layer of the sample 102 (i.e., physically reworking the sample 102). Rather, "correcting metrology measurements" and similar terms may mean correcting an inaccuracy (e.g., a value / term) in a metrology measurement. However, it should be noted that, in an optional configuration / step, a correcting metrology measurement can be used to physically correct (i.e., rework) a defect (e.g., overlay error) in the sample 102 or prevent future defects, thereby improving yield and / or efficiency in the manufacturing process.

[0056] In one embodiment, the metrology system 100 may be configured to receive one or more first measurement images of one or more first target features 202 (e.g., a higher target feature 202a) on a sample captured by a detector at an initial detector focus position among two or more focus positions. For example, the metrology system 100 may include a controller 106 having one or more processors 110 configured to execute program instructions that cause the one or more processors 110 to execute a metrology recipe (e.g., as shown in FIG. 2A and FIG. 3A ) by receiving one or more first measurement images of one or more first target features 202a on the sample 102 captured by the detector at an initial detector focus position. The initial detector focus position may be the focus position shown in FIG. 2A (or FIG. 3A ), and may be a focus position that allows for a focused image of the higher target feature 202a, as shown in FIG. 2A (or FIG. 3A ).

[0057] Continuing with the above example, metrology system 100 can be configured to measure the lateral deflection and / or tilt of a stage element (e.g., coarse positioning stage 208, fine positioning stage 212, and the like) before and / or after adjusting a focal position of the stage element. For example, controller 106 can be further configured to execute program instructions that cause one or more processors 110 to execute a metrology recipe by using one or more proximity sensors to measure / receive one or more first lateral positions of the stage element relative to the optical axis of the imaging system when the stage element is in an initial detector focal position. The measured lateral deflection and / or tilt of the stage element can be used (e.g., mathematically and / or mechanically) to at least partially correct (or prevent) an inaccuracy in a metrology measurement.

[0058] Continuing with the above example, metrology system 100 may be configured to measure one or more first lateral positions of a stage element of imaging system 104 using one or more proximity sensors 222 when a stage element (e.g., coarse positioning stage 208) is in an initial detector focus position. For example, the one or more first lateral positions may include (or be derived from) the proximity sensor gap 224a measurement shown in FIG. 2A . For example, controller 106 may be further configured to execute program instructions that cause one or more processors 110 to execute a metrology recipe by receiving one or more first lateral positions of the stage element relative to optical axis 210 of imaging system 104 using one or more proximity sensors 222 when the stage element is in the initial detector focus position.

[0059] Continuing with the above example, metrology system 100 can be configured to adjust the focus position of at least one of the one or more detectors by moving the stage element an axial adjustment distance from an initial detector focus position to a secondary detector focus position. For example, note how at least coarse positioning stage 208 is lower in Figures 2B, 2C, 3B, and 3C than in Figures 2A and 3A. This lower position can correspond to a lower focal plane position of a detector used to capture (e.g., focus on) one or more target features 202 (e.g., target feature 202b below Figures 2B or 3B) according to a metrology recipe. For example, controller 106 can be further configured to execute program instructions that cause one or more processors 110 to execute a metrology recipe by adjusting the focus position of at least one of the one or more detectors by moving the stage element an axial adjustment distance along optical axis 210 from an initial detector focus position to a secondary detector focus position.

[0060] Continuing with the above example, metrology system 100 can be configured to measure one or more second lateral positions of the stage element using one or more proximity sensors 222 when the stage element is in the secondary detector focus position. For example, the one or more second lateral positions can include (or be derived from) the proximity sensor gap 224b measurement of FIG. 2B or FIG. 3B . Note that proximity sensor gap 224a is smaller than proximity sensor gap 224a. The difference between one or more proximity sensor gaps 224a and one or more proximity sensor gaps 224b can be used to determine a lateral offset and / or tilt of a stage element of imaging system 104 (e.g., coarse positioning stage 208). For example, the controller 106 may be further configured to execute program instructions that cause the one or more processors 110 to execute a metrology recipe by using one or more proximity sensors to receive one or more second lateral positions of the stage element relative to the optical axis when the stage element is in the secondary detector focus position.

[0061] Continuing with the above example, the metrology system 100 may be configured to receive one or more second measurement images of one or more second target features 202 (e.g., lower target feature 202 b) on the sample 102 captured at the secondary detector focus position. For example, the controller 106 may be further configured to execute program instructions that cause the one or more processors 110 to execute a metrology recipe by receiving one or more second measurement images of one or more second target features 202 (e.g., lower target feature 202 b) on the sample 102 captured at the secondary detector focus position by at least one of the one or more detectors.

[0062] Continuing with the above example, the metrology system 100 may be configured to determine at least one of: determining a measured lateral offset of a stage element based on at least one or more first lateral positions and one or more second lateral positions; or determining a measured tilt of a stage element based on at least one or more first lateral positions and one or more second lateral positions. For example, the controller 106 may be further configured to execute program instructions that cause the one or more processors 110 to execute a metrology recipe by determining at least one of: determining at least one of a measured lateral offset of a stage element based on at least one or more first lateral positions and one or more second lateral positions; or determining a measured tilt of a stage element based on at least one or more first lateral positions and one or more second lateral position measurements. For example, the determination may be based on a known configuration of the imaging system 104 such that accurate lateral offset and / or tilt determinations can be made based on the one or more lateral position measurements 224 using one or more proximity sensors.

[0063] Continuing with the above example, the metrology system 100 can be configured to determine a metrology measurement between two or more layers of the sample 102 based on one or more first measurement images and one or more second measurement images according to a metrology recipe. For example, a processor 110 can compare a first feature (e.g., a grating) of a target 202 in a first measurement image captured at an initial detector focus position in a first layer of the sample 102 with a second grating in a second measurement image captured in a second layer of the sample 102 (e.g., at a second secondary focus position) to determine a metrology measurement between an ideal, designed alignment of the two layers and a measured misalignment of the two layers. As mentioned throughout this disclosure, metrology measurements themselves can be inaccurate due to, for example, (but not limited to) inaccuracies in the alignment of the stage components of the imaging system 104. For example, the controller 106 can be further configured to execute program instructions that cause the one or more processors 110 to execute the metrology recipe by determining a metrology measurement between two or more layers of the sample 102 based on the one or more first measurement images and the one or more second measurement images.

[0064] Optionally, metrology system 100 can be configured to at least partially correct metrology measurements using at least one of measuring stage element lateral deflection or measuring stage element tilt. For example, an inaccuracy in a metrology measurement can be at least partially corrected (prevented) mathematically or mechanically. For example, by receiving the lateral deflection of a stage element (e.g., a coarse positioning stage) during a change in focus position, the deflection and / or tilt of the stage element can be determined and used to mathematically adjust / update / correct the metrology measurement to compensate for the inaccuracy in the metrology measurement caused by the deflection and / or tilt of the stage element. In this regard, an updated metrology measurement can be determined based on a metrology recipe. In another example, the lateral deflection and / or tilt can be at least partially prevented (or corrected (e.g., compensated)) mechanically by a fine adjustment stage 226 (as shown in FIG. 2A ) and / or a coarse adjustment stage 228 (as shown in FIG. 3A ). Fine adjustment stage 226 and / or coarse adjustment stage 228 may be capable of adjusting the angle / tilt and / or lateral position of a stage element to at least partially compensate for misalignment of the stage element (e.g., misalignment due to a change in the focal position of a stage element and / or jitter over time). It should be noted that the aforementioned mechanical adjustments may be performed before capturing one or more second measurement images, such that the determined metrology measurement is corrected (prevented) and mathematical adjustments / updates / corrections may not be required. It should also be noted that in some embodiments, a combination of mathematical and mechanical corrections for misalignment may be performed by a combination of an adjustment stage (e.g., a fine adjustment stage) and one or more proximity sensors. For example, one or more proximity sensors may be adjusted for an initial proximity sensor gap 224a, but while the adjustment stage mechanically adjusts the element to at least partially correct the measured proximity sensor gap 224a, jitter over time may have added additional misalignment to the system. Using additional proximity sensor gap measurements measured at or near the time new (eg, second) measurement images are received (eg, proximity sensor gap 224c of FIG. 2C ), metrology measurements associated with the new measurement images may be further mathematically corrected.

[0065] It should be noted that Figures 2A through 3C are for illustrative purposes only and that proximity sensor 222 may be positioned at any number of locations configured to measure a lateral position of a stage element. For example, proximity sensor 222 may be positioned within or adjacent to frame 204 so that it can measure the position of, for example, coarse positioning stage 208. In another example, proximity sensor 222 may be positioned in a location that measures the lateral position of fine positioning stage 212, such as within or adjacent to coarse positioning stage 208. Proximity sensor 222 may be structurally coupled to any element that provides for measuring a lateral position of a stage element. For example, proximity sensor 222 may be structurally coupled to the frame, coarse positioning stage, or any other element of metrology system 100. Proximity sensor 222 may be positioned to measure more than one direction of misalignment of a stage element (e.g., both lateral X and Y directions of a stage element).

[0066] 2A-2C, a metrology system for fine-tuning stage 226 to at least partially correct and / or prevent misalignment of stage components is generally described.

[0067] It should be noted that in some embodiments, the objective lens positioning stage is any element configured for positioning the objective lens, or an element structurally closely associated therewith. For example, the objective lens positioning stage may include at least one of a fine positioning stage or a coarse positioning stage. In another example, the objective lens positioning stage may include at least one of a fine positioning stage, a coarse positioning stage, a fine positioning stage driver, a coarse positioning stage driver, a fine adjustment stage, a coarse adjustment stage, a frame, an air bearing, or a thin flexure arm.

[0068] It should be noted that fine adjustment stage 226 is shown positioned between objective lens 218 and fine positioning stage 212, but can be positioned in any number of positions to ultimately allow adjustment / movement of objective lens 218 or other stage components that affect focus. For example, fine adjustment stage 226 can be located / positioned between fine positioning stage driver 220 and fine positioning stage 212. For example, such a position (not shown) can allow fine adjustment stage 226 to correct a calibration fine positioning stage misalignment by mechanically moving the fine positioning stage to adjust for lateral offset and / or tilt. In this regard, objective lens 218 can be moved along with fine positioning stage 212 and similarly mechanically aligned.

[0069] FIG2A illustrates an imaging system in a first position according to one or more embodiments of the present invention. FIG2B illustrates an imaging system in a second, misaligned position according to one or more embodiments of the present invention. FIG2C illustrates an imaging system in a third position at least partially corrected by a fine adjustment stage according to one or more embodiments of the present invention.

[0070] For example, as described above, a measured lateral offset (e.g., a lateral offset of a measurement stage element) and / or a measured tilt (e.g., a tilt of a measurement stage element) can be determined and used to determine how much to adjust / move a stage element (which may be a stage component different from or the same as the measurement stage element) (e.g., coarse positioning stage 208 and / or objective lens 218) to at least partially prevent (or correct) the measured lateral offset and / or tilt. In this regard, a measured lateral offset of 20 nanometers in a positive radial X direction can be corrected by moving the objective lens 20 nanometers in a negative radial X direction. For example, a metrology measurement can theoretically be completely accurate if all misalignment is measured and fully mechanically corrected by an adjustment stage (e.g., fine adjustment stage 226) before capturing one or more measurement images. The adjustment stage can perform adjustments by any movable components it may include, such as actuators, motors, PZTs, and the like.

[0071] It should be noted that fine adjustment stage 226 can be operatively and / or structurally coupled to fine adjustment stage 212 and / or objective lens 218 (e.g., structurally coupled between fine adjustment stage 212 and objective lens 218). As shown in figures (e.g., FIG. 2C ), fine adjustment stage 226 can be configured to adjust the tilt and / or lateral offset of objective lens 218 relative to one of optical axes 210.

[0072] In some embodiments, similar to fine adjustment stage 226, coarse adjustment stage 228 can also be used to adjust the lateral offset and / or tilt of frame 204 and / or coarse adjustment stage 208 to at least partially correct a lateral offset or tilt of a stage component. For example, referring now to Figures 3A-3C, a metrology system 100 for at least partially correcting and / or preventing misalignment of a stage component is generally described with respect to coarse adjustment stage 228.

[0073] Figure 3A illustrates an imaging system in a first position according to one or more embodiments of the present invention. Figure 3B illustrates an imaging system in a second, misaligned position according to one or more embodiments of the present invention. Figure 3C illustrates an imaging system in a third position at least partially corrected by coarse adjustment stage 228 according to one or more embodiments of the present invention.

[0074] For example, as described above, a measured lateral offset and / or measured tilt can be determined and used to determine the extent to which a stage component (e.g., frame 204; coarse positioning stage 208) should be adjusted / moved to at least partially prevent (or correct) the measured lateral displacement and / or measured tilt of the stage component. In this regard, FIG. 3C may be a diagrammatic depiction of imaging system 104 after adjusting a lateral position (e.g., to compensate for a lateral offset) and a tilt (e.g., to compensate for a tilt) of a stage component (e.g., frame 204, coarse positioning stage 208, or the like).

[0075] It should be noted that throughout the present invention, "at least partially correcting" steps / operations and the like by mechanically adjusting the stage (e.g., coarse adjustment stage 228 and / or fine adjustment stage 226) may occur before "measuring one or more" images (e.g., secondary images) steps / operations and the like, so that the second measured image has been at least partially corrected (e.g., correcting for misalignment of the stage elements) before determining the "metrological measurement" steps / operations and the like; therefore, one inaccuracy in the "metrological measurement" may have been "at least partially corrected" (e.g., prevented) without necessarily requiring another "correction" step / operation.

[0076] In some embodiments, imaging system 104 may include one or more detectors for imaging one or more target features 202 according to a metrology recipe. For example, one or more proximity sensors may be configured to measure the lateral position of a stage element as the objective lens positioning stage moves along the optical axis and / or adjusts the axial position of a focal plane. For example, a detector may be detector assembly 122 of FIG. 2B . In another example, a detector may include one or more pixel sensors (e.g., a 2D sensor, a camera, a focal plane array (FPA), or the like). One or more of the stage elements described herein (e.g., any element of imaging system 104) may be configured to determine the axial position of a focal plane of one or more detectors of imaging system 104. It should be noted that any combination of elements may be used to control the axial position of sample 102 within imaging system 104. For example, the axial position of sample 102 may be adjusted via sample stage 108 (e.g., according to a metrology recipe). As another example, the focal position of the sample 102 may be controlled by adjusting a position of one or more elements of the light collection path 142 (see FIG. 1B ), such as, but not limited to, the objective lens 124 (which may be the objective lens 218 of FIG. 2B ).

[0077] It should be noted that each detector of the one or more detectors may have a maximum focal plane adjustment distance separating them. For example, a higher target feature 202a may require a detector imaged at a higher focal plane, and a lower target feature 202a may require a detector imaged at a lower focal position (e.g., the same detector or a different detector) in order to image each target feature 202 in focus. The difference between the higher and lower focal planes may be a maximum focal plane adjustment distance, which may be measured relative to the target feature (e.g., vertically) (i.e., rather than the distance the stage / optical element moves). For example, the stage element may move an axial distance that is greater or less than the focal plane adjustment distance between the two focal planes. In one example, each detector may be configured to capture images at two or more focal planes along an optical axis 210 of the imaging system 104 through an objective lens 218, where the focal plane of one detector may be different from the focal plane of another detector.

[0078] It should be noted that throughout the present disclosure, objective lens 218 may refer to an objective subsystem including one or more stages / optical elements (such as lenses).

[0079] FIG. 1C illustrates a diagram of a metrology system having two or more detectors according to one or more embodiments of the present invention.

[0080] In some embodiments, the one or more detectors are two or more detectors 122. For example, the imaging system 104 may include at least two detectors 122, such as a first detector 122 and a second detector 122, as shown in FIG1C . For example, as shown in FIG1C , one or more beam splitters 134 may be used to split the collection path 142 into two or more channels, each channel having at least one detector 122. For example, the metrology system 100 may be a dual-detector (e.g., dual-camera) system, in which the first detector 122 may capture an image of a first target feature 202a in a first focal plane, and the second detector 122 may adjust its second focal plane to capture an image of a second target feature 202b without moving the first focal plane. In this regard, when combined with at least some of the benefits of the present invention, a dual-detector imaging system 104 may allow for efficient, rapid, and simultaneous image capture of many target features (e.g., tall targets). For example, the air bearing 206, proximity sensor 222, and / or an adjustment stage in combination with two detectors (e.g., coarse adjustment stage 228) can allow for fast, efficient, and / or accurate metrology measurements of tall targets (e.g., height differences of at least 20, 50, 100, 500, 1000, or 2000 microns). For example, such a combination can achieve at least one of a greater maximum focal plane adjustment distance or a more accurate metrology measurement.

[0081] In one embodiment, a metrology system having two or more detectors is configured to determine a new metrology measurement based on one or more new first images and one or more new second images. For example, the new metrology measurement can be combined with a metrology measurement (e.g., the first metrology measurement) to obtain a more accurate metrology measurement.

[0082] In another embodiment, a metrology system having two or more detectors is configured to determine an averaged overall metrology measurement based on the new metrology measurement and the metrology measurement, such that the averaged overall metrology measurement has an improved signal-to-noise ratio compared to the metrology measurement. For example, a dual-detector metrology system can be configured to obtain metrology measurements multiple times and average the metrology measurements to obtain a single metrology measurement (e.g., the averaged overall metrology measurement) with an improved signal-to-noise ratio.

[0083] In one example, the controller 106 is further configured to execute program instructions that cause the one or more processors to also execute the metrology recipe by: determining a new metrology measurement (e.g., using the aforementioned operations / configurations / steps to obtain a metrology measurement) based on one or more new first measurement images and one or more new second measurement images; and determining an averaged overall metrology measurement based on the new metrology measurement and the metrology measurement, such that the averaged overall metrology measurement has an improved signal-to-noise ratio compared to the metrology measurement. For example, a dual-camera metrology system 100 can allow for efficient capture of measurement images of various target features in various layers of a sample by using one detector positioned at or near a focal length corresponding to the lower target feature 202a and a second detector positioned at or near a focal length corresponding to the higher target feature 202b, thereby reducing the time and distance a detector must travel. Furthermore, multiple metrology measurements can be determined and averaged, resulting in an improved (e.g., higher) signal-to-noise ratio (SNR) of the averaged metrology measurement. Benefits include the ability to efficiently perform high metrology via a larger and / or faster focus adjustment.

[0084] Referring again to FIG. 1A , it should be noted herein that one or more components of the metering system 100 may be communicatively coupled to various other components in the metering system 100 in any manner known in the art.

[0085] In another embodiment, using images and lateral positions to determine a metrology measurement associated with a target on the sample 102 includes: using images to determine a metrology measurement based on a relative position of the feature 202 in two or more focal planes; and correcting the metrology measurement by compensating for lateral offset of the objective positioning stage between the two or more objective positions.

[0086] In another embodiment, the objective lens positioning stage is further configured to adjust at least one of a lateral position or a tilt of the objective lens 218, wherein using the image and the lateral position to determine a metrological measurement associated with a target on the sample 102 includes: using the objective lens positioning stage to adjust at least one of the lateral position or the tilt of the objective lens 218 based on the lateral position of the objective lens positioning stage to align the fields of view of the images captured at two or more objective lens positions within a selected tolerance before capturing the images; and using the images to determine the metrological measurement based on the relative position of the features 202 on the two or more focal planes.

[0087] In another embodiment, the controller 106 includes one or more processors 110 configured to execute program instructions maintained on a memory medium 112. In this regard, the one or more processors 110 of the controller 106 may perform any of the various program steps described herein. Furthermore, the controller 106 may be communicatively coupled to any component of the metrology system 100. For example, the controller 106 may be communicatively coupled to the imaging system 104 to receive images from the imaging system 104 and / or control adjustable components of the imaging system 104 to align the sample 102 within selected alignment tolerances. Furthermore, the controller 106 may determine a metrology measurement associated with two or more layers of the sample 102 based on the measurement images received from the imaging system 104.

[0088] Reference is now made to metrology system 100 in the context of overlay metrology. In some embodiments, as applicable to various embodiments and examples of the present invention, according to a metrology recipe, the metrology system is an overlay metrology system, the metrology measurement is an overlay error, the target is an overlay target, and the feature is an overlay feature. For example, features 202a and 202b in Figures 2A through 3C may be overlay target features 202 (e.g., in a grating-on-grating overlay metrology recipe).

[0089] In one embodiment, the metrology system 100 is a 3D overlay metrology system 100 configured to scan (capture images, receive detection signals) while adjusting the axial position of a focal plane of one or more detectors along a Z direction of an optical axis. For example, a 3D overlay error (offsets in the X, Y, and Z directions) is generated / determined based on multiple detection signals received along multiple focal planes. Furthermore, as described throughout this disclosure with respect to metrology measurements, inaccuracies in the 3D overlay error can be at least partially corrected (or prevented) mathematically and / or mechanically.

[0090] FIG4 illustrates a flow chart of a method 400 for overlay metrology according to one or more embodiments of the present invention. It should be noted herein that the steps of method 400 may be performed in whole or in part by metrology system 100. However, it should be further appreciated that method 400 is not limited to metrology system 100, as additional or alternative system-level embodiments may perform all or part of the steps of method 400.

[0091] In step 402, a lateral position of a stage component of a metrology system 100 is received from one or more proximity sensors. For example, the lateral position can be measured relative to an optical axis.

[0092] In step 404, the objective lens positioning stage is moved along an optical axis to two or more objective lens positions to receive images of two or more focal planes.

[0093] In a step 406, when the objective positioning stage is at two or more objective positions, the image and lateral position of the stage element are used to determine a metrology measurement associated with a target on a sample, the target comprising features on two or more focal planes.

[0094] With reference now generally to metering system 104, the various components are described in greater detail below.

[0095] The one or more processors 110 of a controller 106 may comprise any processing element known in the art. In this regard, the one or more processors 110 may comprise any microprocessor-type device configured to execute software algorithms and / or instructions. In one embodiment, the one or more processors 110 may comprise a desktop computer, mainframe computer system, workstation, video computer, parallel processor, or any other computer system (e.g., a network computer) configured to execute a program configured to operate the metering system 100, as described herein. It should be further understood that the term "processor" may be broadly defined to encompass any device having one or more processing elements that execute program instructions from a non-transitory memory medium 112. Furthermore, the steps described throughout this disclosure may be performed by a single controller 106 or, alternatively, by multiple controllers. Furthermore, the controller 106 may comprise one or more controllers housed in a common housing or multiple housings. In this manner, any controller or combination of controllers may be separately packaged as a module suitable for integration into the metering system 100. Additionally, the controller 106 may analyze data received from the detector assembly 122 and feed the data to additional components within the metrology system 100 or external to the metrology system 100 .

[0096] The memory medium 112 may comprise any storage medium known in the art suitable for storing program instructions executable by the associated one or more processors 110. For example, the memory medium 112 may comprise a non-transitory memory medium. As another example, the memory medium 112 may include, but is not limited to, a read-only memory, a random access memory, a magnetic or optical memory device (e.g., a disk), a magnetic tape, a solid-state drive, and the like. It should be further noted that the memory medium 112 may be housed in a common controller housing along with the one or more processors 110. In one embodiment, the memory medium 112 may be located remotely relative to the physical location of the one or more processors 110 and the controller 106. For example, one or more processors 110 of the controller 106 may access a remote memory (e.g., a server) accessible via a network (e.g., the Internet, an intranet, and the like). Therefore, the above description should not be construed as limiting the present invention and is merely illustrative.

[0097] Those skilled in the art will recognize that the components (e.g., operations), devices, and articles described herein, and their accompanying discussions, are provided as examples to clarify the concepts and to allow for various configuration modifications. Therefore, as used herein, the specific examples described and the accompanying discussions are intended to represent their more general class. Generally speaking, the use of any specific example is intended to represent its class, and the exclusion of specific components (e.g., operations), devices, apparatuses, and articles should not be considered limiting.

[0098] Those skilled in the art will appreciate that there are a variety of vehicles (e.g., hardware, software, and / or firmware) by which the procedures and / or systems and / or other techniques described herein can be implemented, and the preferred vehicle will vary depending on the context in which the procedures and / or systems and / or other techniques are deployed. For example, if an implementer determines that speed and accuracy are primary, the implementer may select a primarily hardware and / or software vehicle; alternatively, if flexibility is primary, the implementer may select a primarily software implementation; or alternatively, the implementer may select some combination of hardware, software, and / or firmware. Thus, there are several possible vehicles by which the procedures and / or devices and / or other techniques described herein can be implemented, and no vehicle is inherently superior to another, as utilizing any vehicle is a matter of choice based on the context in which the vehicle will be deployed and the implementer's specific concerns (e.g., speed, flexibility, or predictability) (any of which may vary).

[0099] The above description is presented to enable one of ordinary skill in the art to make and use the invention as provided in the context of a particular application and its requirements. Those skilled in the art will readily appreciate various modifications to the described embodiments, and the general principles defined herein may be applied to other embodiments. Therefore, the present invention is not intended to be limited to the specific embodiments shown and described but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0100] With respect to the use of substantially any plural and / or singular terms herein, one skilled in the art can convert the plural to the singular and / or the singular to the plural as the context and / or application requires. For the sake of clarity, various singular / plural permutations are not explicitly set forth herein.

[0101] All methods described herein may include storing the results of one or more steps of the method embodiments in memory. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results have been stored, they may be accessed in memory and used by any of the method or system embodiments described herein, formatted for display to a user, used by another software module, method, or system, and so on. Furthermore, the results may be stored "permanently," "semi-permanently," "temporarily," or for a period of time. For example, the memory may be random access memory (RAM), and the results may not necessarily be retained in memory indefinitely.

[0102] Upon further consideration, each of the above method embodiments may include any other steps of any other method described herein. In addition, each of the above method embodiments may be performed by any of the systems described herein.

[0103] The subject matter described herein sometimes depicts various components contained within or connected to other components. It should be understood that these depicted architectures are illustrative only, and that numerous other architectures that achieve the same functionality may be implemented. Conceptually, any configuration of components that achieve the same functionality is effectively "associated" so as to achieve the desired functionality. Thus, any two components herein combined to achieve a particular functionality may be considered "associated" with each other so as to achieve the desired functionality, regardless of architecture or intermediary components. Similarly, any two components so associated may also be considered "connected" or "coupled" to each other so as to achieve the desired functionality, and any two components capable of being so associated may also be considered "coupleable" to each other so as to achieve the desired functionality. Specific examples of "coupleable" include, but are not limited to, components that can physically mate and / or physically interact, components that can wirelessly interact and / or wirelessly interact, and / or components that logically interact and / or logically interact.

[0104] Furthermore, it should be understood that the present invention is defined by the appended claims. Those skilled in the art will understand that, in general, the terms used herein and particularly in the appended claims (e.g., the body of the appended claims) are generally intended to be "open" terms (e.g., the term "comprising" should be interpreted as "including, but not limited to," the term "having" should be interpreted as "having at least," etc.). Those skilled in the art will further understand that if a specific number of an introduced claim recitation is intended, such intent will be explicitly recited in the claim, and if not, no such intent exists. For example, to aid understanding, the following appended claims may contain the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed as implying that the introduction of a claim recitation by the indefinite article "a" or "an" limits any particular claim containing such an introduced claim recitation to inventions containing only one such recitation, even if the same claim contains the introduction phrase "one or more" or "at least one" and an indefinite article such as "a" (for example, "a" should generally be interpreted as meaning "at least one" or "one or more"); the same applies to the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should generally be interpreted as meaning at least the recited number (for example, the bare recitation of "two recitations" without other modifiers generally means at least two recitations or two or more recitations). In addition, in instances where a convention similar to “at least one of A, B, and C, and the like” is used, such construction is generally intended to be what one skilled in the art would normally understand (e.g., “a system having at least one of A, B, and C” would include, but not be limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). In instances where a convention similar to “at least one of A, B, or C, and the like” is used, such construction is generally intended to be what one skilled in the art would normally understand (e.g., “a system having at least one of A, B, or C” would include, but not be limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). Those skilled in the art will further understand that any disjunctive term and / or phrase presenting two or more alternatives, whether in the embodiments, claims, or drawings, should be understood to encompass the possibility of including one, either, or both of the alternatives. For example, the phrase "A or B" will be understood to encompass the possibility of "A" or "B" or "A and B."

[0105] It is believed that the present invention and its many attendant advantages will be understood from the foregoing description, and it will be appreciated that various changes may be made in the form, construction, and arrangement of the components without departing from the present invention or sacrificing all of its material advantages. The forms described are for illustration only, and the following claims are intended to encompass and include such changes. Furthermore, it should be understood that the present invention is defined by the appended claims.

[0106] 100:Metering system 102: Sample 104: Imaging System 106: Controller 108: Sample carrier 110: Processor 112:Memory / Memory Media 114: Lighting Source 116: Illumination beam 118: Lighting Path 120:Concentrated beam 122:Detector assembly 124: Objective lens 126: Lighting path lens 128: Lighting adjustment component 134: Beam splitter 136: Light collecting path lens 138: Adjust the light collecting component 142: Light collection path 202a: First target feature 202b: Second target feature 204:Framework 206: Coarse positioning stage support element / bearing 208: Coarse positioning stage 210: Optical axis 212:Precision positioning stage 214: Coarse positioning stage driver 216: Thin flexure arm 218:Objective lens 220: Precision positioning stage driver 222: Proximity sensor 224a: proximity sensor gap 224b: proximity sensor gap 224c: proximity sensor gap 226: Fine adjustment of the stage 228: Coarse adjustment of the stage 400:Method 402: Steps 404: Steps 406: Steps

Claims

1. A measurement system comprising: One objective lens; One or more detectors; An objective stage, structurally coupled to the objective and configured to adjust at least one focal plane of at least one of one or more detectors by movement along an optical axis, a metrology system including the optical axis; and one or more proximity sensors configured to measure the lateral position of a stage element as the objective stage moves along the optical axis, wherein the lateral positions are measured relative to and orthogonal to the optical axis when the objective stage is at each of two or more objective positions, wherein the metrology system is configured to capture images of two or more focal planes by moving the objective stage along the optical axis to two or more objective positions, each focal plane being located at an axial position along and orthogonal to the optical axis of the metrology system, wherein at least two of the two or more focal planes are separated by an axial focal length greater than a depth of field provided by the objective. The metrology system is configured to use the images and lateral positions of the stage elements of the stage element to determine a metrological measurement associated with a target on a sample when the objective positioning stage is located at the two or more objective positions during the implementation of a metrology formula. The target includes features on the two or more focal planes according to the metrology formula. Determining the metrological measurement includes using the measured lateral positions to compensate for at least one of the lateral offset or tilt of the objective positioning stage between the two or more objective positions.

2. The metrology system of claim 1, wherein using such images and such lateral positions to determine the metrological measurement associated with the target on the sample includes: The measurement is determined using these images based on the relative position of one of the features on two or more focal planes; And the measurement is corrected by compensating for the lateral offset of the objective positioning stage between the two or more objective positions.

3. The metrology system of claim 1, wherein the objective positioning stage is further configured to adjust at least one of the lateral position or tilt of the objective, wherein using such images and the lateral position to determine the metrological measurement associated with the target on the sample includes: Based on the lateral position of the objective lens positioning stage, the objective lens is adjusted using the objective lens positioning stage to align the field of view of the images captured at the two or more objective lens positions within a selected tolerance before capturing the images; and the measurement is determined using the images based on the relative position of one of the features on the two or more focal planes.

4. The metrology system of claim 3, wherein the objective positioning stage is configured to adjust at least one of the objective's lateral position or tilt via an adjustment stage.

5. The metrology system of claim 4, wherein the adjustment stage is at least one of a fine adjustment stage or a coarse adjustment stage, wherein the fine adjustment stage is operatively and structurally coupled to and configured to adjust at least one of the lateral position or tilt of a fine positioning stage or an objective lens, wherein the coarse adjustment stage is operatively and structurally coupled to and configured to adjust at least one of the lateral position or tilt of a coarse positioning stage.

6. The metrology system of claim 1, wherein the objective positioning stage includes at least one of a fine positioning stage or a coarse positioning stage, wherein the fine positioning stage is structurally coupled to the objective lens, the objective positioning stage being configured to allow fine movement along one of the optical axes corresponding to a fine adjustment of the focal plane of the one or more detectors, wherein the coarse positioning stage is structurally coupled to at least one of the fine positioning stage or the objective lens, the objective positioning stage being configured to allow coarse movement along one of the optical axes corresponding to a coarse adjustment of the focal plane of the one or more detectors, wherein a maximum focal plane adjustment distance of the objective positioning stage includes at least one of a maximum fine adjustment of the fine positioning stage or a maximum coarse adjustment of the coarse positioning stage.

7. The metrology system of claim 6, wherein the objective positioning stage includes the fine positioning stage, wherein the fine positioning stage is structurally radially supported about the optical axis by two or more thin flexible arms, the two or more thin flexible arms being configured to allow the fine positioning stage to make fine movements along the optical axis and to constrain the fine positioning stage to one-sided translation and a tilt relative to the optical axis when adjusting the focal plane of the one or more detectors.

8. The metering system of claim 7, wherein the two or more thin flexible arms are located in a parallelogram configuration.

9. The measurement system of claim 7, wherein the two or more thin flexible arms are configured to constrain the lateral translation to an accuracy of 5 nanometers and the tilt to an accuracy of 3 microradians.

10. The metrology system of claim 7, wherein the two or more thin flexible arms comprise a first subset of two or more thin flexible walls on a first side of one of the precision positioning stages, and a second subset of two or more thin flexible arms on a second side of one of the precision positioning stages, wherein the second side is opposite to the first side relative to the optical axis.

11. The metrology system of claim 6, wherein the stage element is the precision positioning stage such that the one or more proximity sensors are configured to measure the lateral positions of the precision positioning stage as the objective positioning stage moves along the optical axis.

12. The metrology system of claim 6, wherein the objective positioning stage is configured to allow the maximum fine adjustment of the precision positioning stage to be at least 50 micrometers.

13. The metrology system of claim 6, wherein the objective positioning stage includes the fine positioning stage and a fine positioning stage driver, the fine positioning stage driver being operatively coupled to the fine positioning stage and configured to provide the fine movement of the fine positioning stage along the optical axis corresponding to the fine adjustment of the focal plane.

14. The metering system of claim 13, wherein the precision positioning stage driver is a piezoelectric device (PZT) configured to generate movement of the precision positioning stage when a voltage is applied to the PZT, wherein the PZT is structurally coupled to the precision positioning stage.

15. The metrology system of claim 6, wherein the objective positioning stage includes a coarse positioning stage and a coarse positioning stage driver, the coarse positioning stage driver being operatively coupled to the coarse positioning stage and configured to provide the coarse movement of the coarse positioning stage along the optical axis corresponding to the coarse adjustment of the focal plane.

16. The metrology system of claim 15, wherein the coarse positioning stage is structurally supported radially around the optical axis by air bearings configured to allow the coarse positioning stage to move roughly along the optical axis and to constrain the coarse positioning stage to translate and tilt laterally relative to the optical axis when the focal plane of the one or more detectors is adjusted.

17. The metrology system of claim 15, wherein the stage element is the coarse positioning stage such that the one or more proximity sensors are configured to measure the lateral positions of the coarse positioning stage as the objective positioning stage moves along the optical axis.

18. The metrology system of claim 15, wherein the objective positioning stage is configured to allow the maximum coarse adjustment of the coarse adjustment stage to be at least 500 micrometers.

19. The metrology system of claim 15, wherein the objective positioning stage is configured to allow the maximum coarse adjustment of the coarse adjustment stage to be at least 2000 micrometers.

20. The metrology system of claim 6, wherein the objective positioning stage is configured to allow the maximum focal plane adjustment distance to be at least 2000 micrometers.

21. The metrology system of claim 6, wherein using such images and such lateral positions to determine the metrological measurement associated with the target on the sample includes: It is determined that one of the precision positioning stages can be repeatedly calibrated by lateral offset and / or tilt.

22. For the metrology system of request item 21, at least the calibration shall be used to calibrate the metrology measurement.

23. The metering system of claim 1, wherein, according to the metering formula, at least one of two or more of the sample includes one or more 3D NAND features.

24. The metrology system of claim 1, wherein the metrology system is configured to image a wafer-to-wafer (W2W) bonding sample, and the sample is a W2W bonding sample according to the metrology formula.

25. The metrology system of claim 1, wherein the metrology system is configured to image a die-to-wafer (D2W) bonding sample, and the sample is a D2W bonding sample according to the metrology formulation.

26. The metrology system of claim 1, wherein the metrology system is configured to use at least one of the following for imaging: different illumination polarization, different illumination numerical aperture, different illumination angle, or different illumination wavelength range.

27. The metering system of claim 1, wherein the one or more detectors include a first detector and a second detector, wherein the first detector is configured to capture a first detector image at a first focal plane, and the second detector is configured to capture a second detector image at a second focal plane.

28. The metering system of claim 27, wherein the metering system is further configured to: determine a new metering measurement based on one or more new first images and one or more new second images; and determine an average total metering measurement based on the new metering measurement and the metering measurement, such that the average total metering measurement has an improved signal-to-noise ratio compared to the metering measurement.

29. The metering system of claim 1, wherein, according to the metering formula, the metering system is a stack of metering systems, the metering measurement is a stack of errors, the target is a stack of targets, and the features are stack of features.

30. A metering system with an air bearing, comprising: One objective lens; One or more detectors; An objective positioning stage, structurally coupled to the objective and configured to adjust the focal plane of at least one of one or more detectors by movement along one optical axis of the metrology system; a coarse positioning stage of the objective positioning stage, structurally supported radially around the optical axis by one or more air bearings configured to allow longitudinal movement of the coarse positioning stage along one optical axis, and constraining lateral translation and tilting of the coarse positioning stage relative to the optical axis when adjusting the focal plane of the one or more detectors; and one or more proximity sensors configured to measure multiple lateral positions of the coarse positioning stage relative to and orthogonal to the optical axis when the objective positioning stage is at each of two or more objective positions along the optical axis. The metrology system is configured to acquire images of two or more focal planes by moving the objective positioning stage along the optical axis to two or more objective positions. Each of the two or more focal planes is located at an axial position along the optical axis of the metrology system and orthogonal to one of the optical axes. At least two of the two or more focal planes are separated by an axial focal length greater than a depth of field provided by the objective. The metrology system is configured to, when a metrology formula is implemented and the objective positioning stage is located at the two or more objective positions, use the images and the measured lateral positions of the coarse positioning stage to determine a metrology measurement associated with a target on a sample, the target comprising features on the two or more focal planes according to the metrology formula. Determining the metrology measurement includes using the measured lateral positions to compensate for at least one lateral offset or tilt of the coarse positioning stage between the two or more objective positions.

31. The metrology system of claim 30, wherein the objective positioning stage is configured to allow one of the coarse positioning stages to be coarsely adjusted to at least 500 micrometers.

32. The metering system of claim 30, wherein the one or more air bearings are configured to constrain the lateral translation within an accuracy of five nanometers and the tilt within an accuracy of five microradians.

33. The metrology system of claim 30, wherein the objective positioning stage includes a coarse positioning stage driver that is operatively coupled to the coarse positioning stage and configured to provide coarse movement of the coarse positioning stage along one of the optical axes corresponding to a coarse adjustment of the focal plane.

34. The metering system of claim 33, wherein the coarse positioning stage driver includes at least one of a linear motor operatively coupled to the stage element, or a combination of a rotary motor operatively coupled to the stage element and a drive screw.

35. A method for superimposed measurement, the method comprising: The measurement system receives the lateral position of a stage element of a measurement system from one or more proximity sensors. When the objective positioning stage is at each of two or more objective positions, the lateral positions are measured relative to and orthogonal to an optical axis. The measurement system is configured to adjust the focal position of at least one of the detectors in the measurement system. The measurement system is configured to move along the optical axis via an objective positioning stage to two or more objective positions to capture images of two or more focal planes. Each of the two or more focal planes is located at an axial position along and orthogonal to the optical axis of the measurement system. At least two of the two or more focal planes are separated by an axial focal length greater than a depth of field provided by an objective. The objective positioning stage is moved along the optical axis to the two or more objective lens positions to receive images of two or more focal planes; and when the objective positioning stage is located at the two or more objective lens positions, the images and lateral positions of the stage element are used to determine a metrological measurement associated with a target on a sample, the target comprising features on the two or more focal planes, wherein determining the metrological measurement includes using the measured lateral positions to compensate for at least one of the lateral offset or tilt of the objective positioning stage between the two or more objective lens positions.

36. The method of claim 35, wherein determining the measurement associated with the target on the sample includes: The measurement is determined using the images based on the relative position of one of the features on the two or more focal planes; and the measurement is corrected by using the received lateral position to compensate for the lateral offset of the objective positioning stage between the two or more objective positions.

37. The method of claim 35, wherein the objective positioning stage is further configured to adjust at least one of the lateral position or tilt of the objective, wherein determining the metrology associated with the target further includes: Based on the lateral position of the objective lens positioning stage, the objective lens is adjusted using the objective lens positioning stage to align at least one of the lateral position or the tilt of the objective lens within a selected tolerance before capturing the images; and the measurement is determined using the images based on the relative position of one of the features on the two or more focal planes.

Images